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The primary goal of this work is to develop an efficient analytical tool for the computer simulation of progressive damage in the fiber reinforced composite (FRC) materials and thus to provide the micro mechanics-based theoretical framework for a deeper insight into fatigue phenomena in them. An accurate solution has been obtained for the micro stress field in a meso cell model of fibrous composite. The developed method combines the superposition principle, Kolosov-Muskhelishvili's technique of complex potentials and Fourier series expansion. By using the properly chosen periodic potentials, the primary boundary-value problem stated on the multiple-connected domain has been reduced to an ordinary, wellposed set of linear algebraic equations. The meso cell can include up to several hundred inclusions which is sufficient to account for the micro structure statistics of composite. The presented numerical examples demonstrate an accuracy and high numerical efficiency of the method which makes it to be a promising tool for studying progressive damage in FRCs. By averaging over a number of random structure realizations, the statistically meaningful results have been obtained for both the local stress and effective elastic moduli of disordered fibrous composite. A special attention has been paid to the interface stress statistics and the fiber debonding paths development, which appear to correlate well with the experimental observations.

An accurate series solution has been obtained for a piece-homogeneous elastic plane containing a finite array of nonoverlapping elliptic inclusions of arbitrary size, aspect ratio, location and elastic properties. The method combines standard MuskhelishviliÕs representation of general solution in terms of complex potentials with the superposition principle and newly derived re-expansion formulae to obtain a complete solution of the many-inclusion problem. By exact satisfaction of all the interface conditions, a primary boundary-value problem stated on a complicated heterogeneous domain has been reduced to an ordinary well-posed set of linear algebraic equations. A properly chosen form of potentials provides a remarkably simple form of solution and thus an efficient computational algorithm. The theory developed is rather general and can be applied to solve a variety of composite mechanics problems. The advanced models of composite involving up to several hundred inclusions and providing an accurate account for the microstructure statistics and fiber-fiber interactions can be considered in this way. The numerical examples are given showing high accuracy and numerical efficiency of the method developed and disclosing the way and extent to which the selected structural parameters influence the stress concentration at the matrix-inclusion interface.

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